Finite Math Examples

$x^{8} - 9 y^{10}$

Step 1

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

${(x^{4})}^{2} - 9 y^{10}$

Step 2

Rewrite $9 y^{10}$ as ${(3 y^{5})}^{2}$ .

${(x^{4})}^{2} - {(3 y^{5})}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x^{4}$ and $b = 3 y^{5}$ .

$(x^{4} + 3 y^{5}) (x^{4} - (3 y^{5}))$

Step 4

Multiply $3$ by $- 1$ .

$(x^{4} + 3 y^{5}) (x^{4} - 3 y^{5})$